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Title: Theorems on the Convergence of Series in Generalized Lommel-Wright Functions
Authors: Paneva-Konovska, Jordanka
Keywords: Bessel
Generalized Bessel-Maitland
Generalized Lommel-Wright Functions
Abel and Tauber Theorems
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 1, (2007), 59p-74p
Abstract: The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized Lommel-Wright functions in the case of large values of the index ν that are used in the proofs of the Cauchy-Hadamard, Abel and Tauber type theorems for the considered series.
Description: Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20
ISSN: 1311-0454
Appears in Collections:2007

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